TY - GEN A1 - Gräser, Carsten A1 - Sander, Oliver T1 - Polyhedral Gauß-Seidel Converges N2 - We prove global convergence of an inexact polyhedral Gau\ss--Seidel method for the minimization of strictly convex functionals that are continuously differentiable on each polyhedron of a polyhedral decomposition of their domains of definition. While being known to be very slow by themselves, such methods are a cornerstone for fast, globally convergent multigrid methods. Our result generalizes the proof of Kornhuber and Krause [2006] for differentiable functionals on the Gibbs simplex. Example applications are given that require the generality of our approach. KW - polyhedral Gauss-Seidel KW - global convergence KW - multigrid methods KW - Allen-Cahn-equation KW - Discontinuous Galerkin methods Y1 - 2010 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/687 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-6879 ER -